"measurement" and "observation" are just as poorly defined as "uncertainty."

Uncertainty is a very precisely defined quantity. It's nothing more and nothing less the standard deviation of an observable. An observable is the eigenvalue of an operator corresponding to a physical quantity. E.g. to make a measurement all you do is record what it is that you're interested in. For example; take out your digital camera and take a picture. For a moment light will enter the iris of the aperture an hit the Charged Coupled Device (CCD). When light hits the screen its basically photons hitting the pixels on the CCD. When that happens the device allows a record of which pixel was struck and what energy of the photon/light struck it. That's how energy and position is measured in this case. Position and energy commute so that you can measure them simultaneously and exactly.

When you run an experiment, say, 100,000 times starting out in the same state and measuring the same observable and record the measurements then you can calculate the standard deviation which is what uncertainty is.

I would consider any use of an operator on the wavefunction as an "observation." As long as the two (or more) operators don't commute, there is going to be Uncertainty depending on which observation is made first, and the accuracy of that measurement.

The uncertainty has nothing to do with accuracy. That's a common misconception.

From the point of view of an experimenter, there are many different sources of uncertainty, ..

Nope. That's not true. The only thing that the uncertainty is a function of is the wave function. Please read the Wikipedia page on uncertainty. See

http://en.wikipedia.org/wiki/Uncertainty_principle Uncertainty is defined as (Note: I don't know how to use Latex enough to put the hat over the variables so just keep in mind that they're there)

[tex]\Delta x \equiv \sigma_x = \sqrt{<x^2> - <x>^2}[/tex]

[tex]\Delta p \equiv \sigma_p = \sqrt{<p^2> - <p>^2}[/tex]

(sorry about the Latex. I did it exactly as

http://oeis.org/wiki/List_of_LaTeX_mathematical_symbols says and it still came out wrong)

Look at the first equation in the Wikipedia page for uncertainty. The uncertainty relationship is

[tex]\sigma_x\sigma_p > \frac{\hbar}{2}[/tex]

--Schrödinger's Cat is not about what people can and can't know--it's about superposition, and as far as I'm concerned, whatever "detects" the decay of the atom and releases the poison is what does the "observation" thereby collapsing the superposition,...

As Griffiths explains about the cat in the box experiment in his QM text

Schrodinger regarded this as patent nonsense, and I think that most physicists would agree with him. There is something absurd about the very idea of a *macroscopic* object being a linear combination of two palpably different states. An electron can be in a linear combination of two palpably different states, but a cat cannot *be* in a linear combination of alive and dead.

You can read more about this in

http://bookzz.org/book/2031469/ca8981Standard deviation is kind of useless if we are talking about a single measurement ...

That's why both uncertainty and probability has nothing to do with single measurements. It only has meaning for an ensemble of measurements or systems.

re -

*this is why they measure large numbers of particles* - Exactly!

but that doesn't mean that the phenomena they describe are necessarily only observed in populations, it still applies on a particle-by-particle basis.

Not uncertainty. All quantum mechanics can do is tell what can happen statistically.